boolean algebra (binary logic)
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Boolean Algebra (Binary Logic)
Theorem
A + 0 = AA + 1 = 1A A A
A * 0 = 0A * 1 = AA * A AA + A = A
A + A’ = 1A * A = AA * A’ = 0
A + B = B + A(A + B) + C = A + (B + C)AB + AC = A(B + C)
A * B = B * A(A * B) * C = A * (B * C)(A + B)*(A + C) = A + BCAB + AC = A(B + C) (A + B) (A + C) = A + BC
Boolean Algebra (Binary Logic)
A’B’ + A’B + AB = A’ + B = Z
A’B’ =>
ZA’B ZA’
B
AB
A + 0 = A A * 0 = 0A + 1 = 1A + A = AA + A’ = 1
A * 1 = AA * A = AA * A’ = 0
A + B = B + A(A + B) + C = A + (B + C)AB + AC = A(B + C)
A * B = B * A(A * B) * C = A * (B * C)(A + B)*(A + C) = A + BC
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
AB
AB
AB + ACB
AC
AB + ACB
ACC C
Boolean Algebra (Binary Logic)
More Theorem (DeMorgan)
(A + B)’ = A’ * B’ (A * B)’ = A’ + B’
Why NAND and NOR gates?
AB
AB
Why NAND and NOR gates?
AB + ACB
AC
AB + ACB
ACC C
Boolean Algebra (Binary Logic)
More Function (Exclusive‐OR)
Z = AB’ + A’B
Boolean Algebra (Binary Logic)
More Function (Exclusive‐OR)
Z = AB’ + A’B Z = A B
ZAB
Boolean Algebra (Binary Logic)
More Function (Exclusive‐OR)
Z = AB’ + A’B Z = A B
ZABA
ZB’
ZA’B
Boolean Algebra (Binary Logic)
Parity circuits: even/odd
Z
ASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)
Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----
ASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)
Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----
Choi = $43 $68 $6F $69
ASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)
Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----
Choi = $43 $68 $6F $69
0100 0011 => ‘C’ = $430100 0011 => C = $430100 0011 => MSB odd parity
ASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)
Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----
Choi = $43 $68 $6F $69
0100 0011 => ‘C’ = $430100 0011 => C = $430100 0011 => MSB odd parity1100 0011 => MSB even parity
ASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)
Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----
Choi = $43 $68 $6F $69
0100 0011 => ‘C’ = $43 0110 1111 => ‘o’ = $6F0100 0011 => C = $430100 0011 => MSB odd parity1100 0011 => MSB even parity
0110 1111 => o = $6F1110 1111 => MSB odd parity0110 1111 => MSB even parity
100 0011 => ‘C’ = $430100 0011 => MSB odd parity
110 1111 => ‘o’ = $6F1110 1111 => MSB odd parity
1100 0011 => MSB even parity 0110 1111 => MSB even parity
P it Ci itParity Circuit
D7 D6 D5 D4 D3 D2 D1 D0 = P
0100 0011 => ‘C’ = $430100 0011 => MSB odd parity1100 0011 => MSB even parity
D6 D5 D4 D3 D2 D1 D0 = P1 0 0 0 0 1 1 = P
Even Parity
1 1 0 0 0 0 1 1
Even Parity
D7 D6 D5 D4 D3 D2 D1 D01 1 0 0 0 0 1 1
Z = A B
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